Ignored input dynamics and a new characterization of control Lyapunov functions

Our objective in this paper is to extend as much as possible the dissipativ ity approach for the study of robustness of stability in the presence of kn own/unknown but ignored input dynamics. This leads us to: give a new characterization of control Lyapunov functions (CLF) where LfV i s upper-bounded by a function of LgV, define the dissipativity approach as assuming the ignored dynamics are dissipative with storage function W and ( known) supply rate w, analyzing closed-loop stability with the sum of a CLF for the nominal part and the storage function W. Stability margin are given in terms of an inequality the supply should sati sfy. Nevertheless, in spite of this extension, we show that the dissipativi ty approach cannot cope with ignored dynamics which have nonzero relative d egree or are nonminimum phase. (C) 2001 Elsevier Science Ltd. All rights re served.